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A multi-item continuous review inventory system with compound Poisson demands

Author

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  • K. Ohno
  • T. Ishigaki

Abstract

In this paper, we consider a multi-item continuous review inventory system with compound Poisson demands under a general cost structure. Excess demand is backlogged and a fixed delivery lag is assumed. A new algorithm for computing an exact optimal policy is derived based upon the policy iteration method (PIM) using properties of the optimal policy. This algorithm reduces substantially computation times in both the policy evaluation and the policy improvement routines of the PIM. In fact, numerical examples show that the computation times of the new algorithm are less than three percent of those of the PIM. Moreover, three joint ordering policies – the (s, c, S), the (R, T) and the (Q, S) policies – are compared with the optimal ordering policy computed by the new algorithm. It is shown that the (Q, S) policy is almost best among the three joint ordering policy and gives more than ten percent higher expected cost rate than the optimal ordering policy. Copyright Springer-Verlag Berlin Heidelberg 2001

Suggested Citation

  • K. Ohno & T. Ishigaki, 2001. "A multi-item continuous review inventory system with compound Poisson demands," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 53(1), pages 147-165, April.
    • Handle: RePEc:spr:mathme:v:53:y:2001:i:1:p:147-165
    DOI: 10.1007/s001860000101
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    Citations

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    Cited by:

    1. S G Johansen & P Melchiors, 2003. "Can-order policy for the periodic-review joint replenishment problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(3), pages 283-290, March.
    2. Young Hyeon Yang & Jong Soo Kim, 2020. "An adaptive joint replenishment policy for items with non-stationary demands," Operational Research, Springer, vol. 20(3), pages 1665-1684, September.
    3. Larsen, Christian, 2009. "The Q(s,S) control policy for the joint replenishment problem extended to the case of correlation among item-demands," International Journal of Production Economics, Elsevier, vol. 118(1), pages 292-297, March.
    4. Minner, Stefan & Silver, Edward A., 2007. "Replenishment policies for multiple products with compound-Poisson demand that share a common warehouse," International Journal of Production Economics, Elsevier, vol. 108(1-2), pages 388-398, July.
    5. Larsen, Christian, 2007. "The Q(s,S) control policy for the joint replenishment problem extended to the case of correlation among item-demands," CORAL Working Papers L-2007-01, University of Aarhus, Aarhus School of Business, Department of Business Studies.
    6. Sivakumar, B., 2008. "Two-commodity inventory system with retrial demand," European Journal of Operational Research, Elsevier, vol. 187(1), pages 70-83, May.
    7. Sandun C. Perera & Suresh P. Sethi, 2023. "A survey of stochastic inventory models with fixed costs: Optimality of (s, S) and (s, S)‐type policies—Continuous‐time case," Production and Operations Management, Production and Operations Management Society, vol. 32(1), pages 154-169, January.

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